Ch. 15--ANOVA
1. Use of flow chart
2. Overview
3. The F test
a. sampling distribution of F
b. F table
c. when to use the F test
i. more than 2 groups
i. F vs. Multiple t-tests
4. Generating Hypotheses for ANOVA
5. Calculating the statistic
a. Conceptual F
i. Total Variance
ii. Between-group variance
iii. Within group variance
iv. Fobt = sb2/ sw2
b. Calculating Fobt
Source of variance SS df s2 (MS) Fobt
Between groups formula k-1 Ssb / dfb sb2/ sw2
Within groups formula N-k Ssw / dfw
Total Formula N-1
SSb =
SSw =
SSt =
Example
is there a difference exam scores as a function of teaching style? 3 different teachers.
X1 X2 X3
52 46 44
57 52 53
55 51 50
59 50 51
6. Evaluating Fobt--compare with fcrit
7. Comparison between F and t
i. testing means
ii. t2 = F
8. Assumptions of ANOVA
i. normal distribution
ii. Homogeneity of variance
iii. Robust
9. Two-way, or Factorial ANOVA
i. Factorial experiment: when two or more factors are assessed
ii. Use a two-way ANOVA
iii. Components to understand:
a. main effects= effect of one IV independent of the other
b. interaction= when the effect of one IV is not the same at all levels of the other IV
iv. F's for main effects
a. IV1 : F = sr2 /sw2
b. IV2 F = sc2 /sw2
c. Interaction: F = src2 /sw2